An electrostatic dust precipitator that is installed in a factory smokestack includes a straight metal wire of length 0.7 m that
is charged approximately uniformly with a total charge 0.8 ×10−7 C. A speck of coal dust (which is mostly carbon) is near the wire, far from both ends of the wire; the distance from the wire to the speck is 1.4 cm. Carbon has an atomic mass of 12 (6 protons and 6 neutrons in the nucleus). A careful measurement of the polarizability of a carbon atom gives the value 1.96 × 10−40 (C · m)/(N/C). (a) Calculate the initial acceleration of the speck of coal dust, neglecting gravity. Your answer must be expressed in terms of , and . You can use other quantities in your calculations, but your final result must not include them. It is convenient to use the "binomial expansion" that you may have learned in calculus, that if . Note that can be negative. (Enter the magnitude. Use the following as necessary: , , , and for the mass of a carbon atom. Use the binomial expansion in your answer.)
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